You can make it using a plastic aquarium plant leaf with a sturdy stem and a suction cup. Stick the stem in the suction cup hole, add aquarium safe glue or silicone if needed, and voila, you've got yourself a betta hammock.

My live Lilly plants double as hammocks with their big wide leaves, so if you'd like to got he live plant route, you can pick up the Lilly bulbs at Wal-Mart for super cheap and grow your own. They take about 3 weeks to sprout initially, but after that, they grow very quickly. Both my Bettas love them, and love to sleep on the leaves.